Enterprise Risk Management Formula Book
Appendix A.6: Probability Distributions: Distributional
families
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Exponential family
A (continuous) random variable 
(multivariate
or univariate) follows a distribution from the exponential family, with vector
parameter 
, if its
probability (density) function can be written in the form:
or equivalently as:
The 
are
automatically determined once the other functions have been chosen because 
. 
is
called the natural parameter.
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